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In the past several decades it has become clear that mechanical (radio-mode) feedback from supermassive blackholes is necessary to moderate the growth of the most massive galaxies in which they reside. In particular, in the cores of galaxy clusters, the evolution of giant elliptical galaxies appears to be primarily governed by black hole feedback. Despite its apparent importance, our understanding of how feedback works is quite incomplete, particularly when it comes to mechanical or radio-mode feedback. In this talk I will discuss two directions that we are pursuing to understand the balance between cooling and feedback in galaxy cluster cores: (i) identifying systems for which feedback appears to not work, in an effort to understand the limitations and failure modes of the feedback/cooling cycle, and (ii) searching for both short- and long-term trends in the importance of AGN feedback, by considering large samples of clusters spanning 10 Gyr in cosmic time. These efforts are made possible by combining data from a variety of X-ray, optical, mm-wave, and radio telescopes, including Chandra, Hubble, James Webb, and the South Pole Telescope. I will conclude with a look towards the future of this field, and highlight some outstanding questions.